Robustness tests for multidimensional poverty comparisons

This paper provides practical tests for the robustness of multidimensional comparisons of well-being. Focussing on counting-type multidimensional poverty measures, I draw on the properties of positive Boolean threshold functions to prove that the space of feasible poverty definitions is finite and can be partitioned into at most (D2 +D)/2 parts, where D is the number of dimensions of well-being spanned by the measure. This provides the foundation for two complementary tests: (i) a bounding approach, which weights each dimension equally; and (ii) stochastic search, where coverage of the space of poverty definitions is assessed via Good-Turing estimates of missing mass. The two methods are applied to a measure encompassing nine dimensions of well-being in Mozambique, revealing persistent regional asymmetries.